
 Predict the maximum speed (velocity) of each ball on each ramp. How would this speed change if each ball’s mass was doubled? ASSUMPTION: assume there is no friction and that all the potential energy you calculated in question 1 is transformed into kinetic energy – PE = KE. Use the following equation.KE= ½ m v^{2 }
You want to calculate v maximum speed
v = [KE/ ½ m]^{½}
This means divide the KE by half the mass and then take the square root.
 Predict the maximum speed (velocity) of each ball on each ramp. How would this speed change if each ball’s mass was doubled? ASSUMPTION: assume there is no friction and that all the potential energy you calculated in question 1 is transformed into kinetic energy – PE = KE. Use the following equation.KE= ½ m v^{2 }
Max v for 20 lb. ball  Max v for 40 lb. ball  
Ramp 1  
Ramp 2  
Ramp 3 

 Predict the maximum speed (velocity) of each ball on each ramp. How would this speed change if each ball’s mass was doubled? ASSUMPTION: assume there is no friction and that all the potential energy you calculated in question 1 is transformed into kinetic energy – PE = KE. Use the following equation.KE= ½ m v^{2 }
You want to calculate v maximum speed
v = [KE/ ½ m]^{½}
This means divide the KE by half the mass and then take the square root.
 Predict the maximum speed (velocity) of each ball on each ramp. How would this speed change if each ball’s mass was doubled? ASSUMPTION: assume there is no friction and that all the potential energy you calculated in question 1 is transformed into kinetic energy – PE = KE. Use the following equation.KE= ½ m v^{2 }
Max v for 20 lb. ball  Max v for 40 lb. ball  
Ramp 1  
Ramp 2  
Ramp 3 
Section 2 (Each of the green balls has a center of mass placed at 20 feet high). While each ramp looks identical, each ramp has a different amount of friction.

 Which ramp has the greatest friction?
 Suppose each green ball weighs 10 lbs. Assuming there is no friction, calculate the potential energy for each ball on each ramp.
 Again assuming there is no friction; predict the maximum speed of the ball on each ramp. On which ramp does the ball come closest to achieving this max speed?